Triple

Target class: generalization of Riemannian geometry
Context triple: [Weyl geometry, instanceOf, generalization of Riemannian geometry]

• A. pseudo-Riemannian manifold
  A pseudo-Riemannian manifold is a smooth manifold equipped with a nondegenerate, symmetric metric tensor of arbitrary signature that allows measurement of lengths and angles, including those with indefinite sign as in spacetime geometry.
• B. branch of differential geometry chosen
  A branch of differential geometry is a specialized area of study within differential geometry that focuses on analyzing smooth manifolds and related geometric structures using differential and integral calculus techniques.
• C. differential geometric object
  A differential geometric object is a mathematical entity, such as a manifold, tensor, or connection, defined on smooth spaces and characterized by properties that are invariant under smooth coordinate transformations.
• D. Lorentzian manifold
  A Lorentzian manifold is a smooth manifold equipped with a metric tensor of signature \((-+\cdots+)\) (or its variants) that models spacetime in general relativity by distinguishing timelike, spacelike, and null directions.
• E. curvature tensor
  A curvature tensor is a multilinear mathematical object in differential geometry that measures how much a space (or manifold) deviates from being flat by quantifying the failure of vectors to return to their original direction after parallel transport around infinitesimal loops.
• F. None of above.